Computation Methods in Statistical and Quantum Mechanics

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Research will be conducted on the development and application of computational methods and algorithms in statistical mechanics and related areas in quantum condensed matter physics. The development of methods predominantly features computation of subdominant transfer matrix eigenvalues and excited state energies, where the main applications will be (i) universal amplitudes in critical phemonena and quantum spin chains; (ii) the relaxation time spectrum of stochastic dynamics; (iii) models for Monte Carlo error analysis; and, (iv) excited state properties of Lennard-Jones boson clusters. Another topic is the universality with respect to surface fluctuations (geometric and other) of amplitudes characterizing wetting layers at bulk criticality. Lastly, we propose to develop a systematically improvable approximation scheme for the computation of the finite temperature thermodynamics of quantum chains. %%% Theoretical and computational research will be done to improve computational techniques used in dealing with the interactions of large numbers of particles. A number of different systems will be studied to demonstrate the developed techniques. The successful completion of this project will provide techniques which are applicible to a variety of important computationally intensive problems.